May 23, 2010

Physics & Poker—Lesson 1: Special Relativity

I've always been a big science geek, even though my career took me in other directions. My all-time favorite test question from every course I took in college and law school was this gem from my honors physics course:

You are driving down a highway and see a stoplight in the distance, with a police car stopped on the side of the road. The light is green, so you keep driving. Suddenly, you see the police car in your rearview mirror, lights flashing. You pull over and get a ticket for running a red light! Now, assuming you and the police officer are both telling the truth about what happened, do you have a defense to the ticket for running a red stoplight? If so, why should you probably not use that defense in court?

Now, the answer is fairly straightforward if you've been studying special relativity for a few weeks. The question is simply a dressed-up inquiry regarding the different frames of reference for the car driver and the police officer, as expressed in terms of a redshift / blueshift of the color of the stoplight. The police officer is stationary relative to the light, while the car driver is approaching the light and thus experiences a blueshift—the light from the stoplight appears more compressed to the car driver, so the light shifts to a higher frequency (the more common redshift is the opposite effect—as a light source moves away, it will shift to a lower frequency). If the car driver is driving toward the stoplight at a fast enough speed, the color of the stoplight will shift from red to green. So yes, it's entirely possible that both the car driver and the police officer can tell the truth about whether they viewed the stoplight as green or red. The only problem for the car driver is that he would have needed to be driving at something approaching 2/3 to 3/4 the speed of light (relative to the police officer) for that magnitude of blueshift to have occurred—which would mean getting one heck of a speeding ticket just to prove one hadn't run a red stoplight.

The arms of a spiral galaxy exhibit redshifts and blueshifts

as the galaxy rotates relative to an observer on Earth.

So what do special relativity and redshifts / blueshifts have to do with poker? I was reminded of the importance of recognizing different frames of references in what turned into a big hand Friday night. I was in the cutoff with Ts9s, and a fairly tight player in early position raised to $12, pretty standard for the table. There were a couple of callers to me, so I called as well. The flop was T-8-3 with two hearts. The original bettor made a half pot bet, it folded to me, and I called. Now, I often raise with top pair in these situations, but I wasn't sure where I stood and I wanted to keep the pot small and reevaluate as we went along. The turn was an offsuit 6, giving me a gutshot straight draw as backup, but I still wasn't too excited about the hand, so I flat-called another 1/2 pot bet, and began to wonder if I could even make a crying call on the river. The river, however, saved me, putting out a non-heart 9 for top two pair. My opponent led out again for the same bet as his turn bet, looking like a value bet. I raised enough to put my opponent all-in. It wasn't a lot more, and I was fairly confident I was ahead, not to mention I had pretty well committed myself to this raise for value by how I played the hand. My opponent thought a bit, then called and showed KK. He seemed genuinely shocked to see my hand, saying several times, "I thought you had a busted flush draw."

So what does this hand have to do with special relativity? Well, the common connection is the concept of "frames of reference". Things that appear one way for you may not appear the same way for another player. I was playing small ball with top pair-weak kicker, and value raised the river when I caught top two pair. My hand, T9s, seemed fairly obvious to me, but I figured an overpair would still make a crying call. I certainly didn't think my opponent would be all that shocked to see T9s given the way the hand played out. To my opponent, however, my line of calling the flop and turn, then raising the river, looked exactly like how he would have played a busted flush draw in late position. Also, my opponent would never have flat-called with top pair on the flop or the turn. So, from his frame of reference, my hand was almost certainly a draw, and the only credible draw was the flush draw, which didn't hit.

A lot of poker commentators have talked about a concept related to frames of reference—"levels of thinking".* Here, my opponent seemed stuck on Level 2—"What does my opponent have?"—and made the determination I had a flush draw based on how he would play certain hands in my position. What my opponent forgot—and what we all tend to forget—is that other players may play hands differently than we do, or differently than the "standard line". In fact, I would argue that assuming another player shares our frame of reference at the poker table—i.e., plays hands the same way, has the same level of poker knowledge, has the same regard/disregard for money, or is playing for the same reasons—is one of the biggest errors a serious player can commit.

So, when trying to interpret an opponent's play at the poker table, the relevant question is never "How would I play my opponent's hand?" or "What would Jesus Ferguson do?" (WWJFD). Instead, the correct question is "How would this player play this hand?" Sometimes, the answer may surprise you.